Algebra is hard

For certain values of k and m, the system

3a + 2b = 2

6a + 2b = k + 3a + mb

has infinitely many solutions (a,b). What are k and m?

Guest May 7, 2023

#1**0 **

We can only have infinitely many solutions (a,b) when both of our equations are identical. We have:

3a + 2b = 2

6a + 2b = k + 3a + mb

If we subtract 3a from both sides of our lower equation we get

3a + 2b = k + mb

Now, the left-hand side of both equations is identical.

For the right-hand side, we can set:

k+mb=2

We can see that m must be 0, as if it is not we will have a variable with b, so our result will vary based on b, and not always be 2. This cannot be so we need m=0 as it will cancel out b. Then, we are left with k+0(b)=2 k=2.

Hence, we have that m=0 and k=2.

I hope this helped!

Guest May 8, 2023

edited by
Guest
May 8, 2023